Class 9 Exam > Class 9 Questions > If the length of each side of rhombus is 15 c...
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If the length of each side of rhombus is 15 cm and one of its diagonals is 24 cm what is length of other diagonal?
- a)16 cm
- b)14 cm
- c)18 cm
- d)12 cm
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the length of each side of rhombus is 15 cm and one of its diagonal...
Given information:
- Length of each side of the rhombus = 15 cm
- Length of one diagonal = 24 cm
To find: Length of the other diagonal
Properties of a rhombus:
1. All sides of a rhombus are equal in length.
2. The diagonals of a rhombus bisect each other at right angles.
Using these properties, we can solve the problem.
Solution:
Let's denote the length of the other diagonal as 'd'.
Step 1: Find the length of the other side of the rhombus.
Since all sides of a rhombus are equal in length, the length of each side is 15 cm.
Step 2: Find the length of the diagonals.
The diagonals of a rhombus bisect each other at right angles. This means that they divide the rhombus into four congruent right-angled triangles.
Using the Pythagorean theorem, we can find the length of the diagonals.
In each right-angled triangle, the hypotenuse is the length of the diagonal, and the two legs are the lengths of the sides of the rhombus.
Applying the Pythagorean theorem:
(15/2)^2 + (d/2)^2 = (24/2)^2
225/4 + d^2/4 = 144
225 + d^2 = 576
d^2 = 576 - 225
d^2 = 351
Taking the square root of both sides:
d = √351
d ≈ 18.7 cm (rounded to the nearest tenth)
Step 3: Choose the correct option.
The question asks for the length of the other diagonal, so the answer is approximately 18.7 cm, which is closest to option (c) 18 cm.
Therefore, the correct answer is option (c) 18 cm.
- Length of each side of the rhombus = 15 cm
- Length of one diagonal = 24 cm
To find: Length of the other diagonal
Properties of a rhombus:
1. All sides of a rhombus are equal in length.
2. The diagonals of a rhombus bisect each other at right angles.
Using these properties, we can solve the problem.
Solution:
Let's denote the length of the other diagonal as 'd'.
Step 1: Find the length of the other side of the rhombus.
Since all sides of a rhombus are equal in length, the length of each side is 15 cm.
Step 2: Find the length of the diagonals.
The diagonals of a rhombus bisect each other at right angles. This means that they divide the rhombus into four congruent right-angled triangles.
Using the Pythagorean theorem, we can find the length of the diagonals.
In each right-angled triangle, the hypotenuse is the length of the diagonal, and the two legs are the lengths of the sides of the rhombus.
Applying the Pythagorean theorem:
(15/2)^2 + (d/2)^2 = (24/2)^2
225/4 + d^2/4 = 144
225 + d^2 = 576
d^2 = 576 - 225
d^2 = 351
Taking the square root of both sides:
d = √351
d ≈ 18.7 cm (rounded to the nearest tenth)
Step 3: Choose the correct option.
The question asks for the length of the other diagonal, so the answer is approximately 18.7 cm, which is closest to option (c) 18 cm.
Therefore, the correct answer is option (c) 18 cm.
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Community Answer
If the length of each side of rhombus is 15 cm and one of its diagonal...
∵ Diagonals of a rhombus bisect each other at 90°
In ΔAOD
AD = 15 cm, AC = 12 cm,
∴ BD = 2OD
= 2 × 9 = 18 cm
In ΔAOD
AD = 15 cm, AC = 12 cm,
∴ BD = 2OD
= 2 × 9 = 18 cm
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If the length of each side of rhombus is 15 cm and one of its diagonals is 24 cm what is length of other diagonal?a)16 cmb)14 cmc)18 cmd)12 cmCorrect answer is option 'C'. Can you explain this answer?
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